A few general things that can help with the label issues. These are things I have read in different threads, haven't had to try them, so they may or may not help.
If you have to pay your bill down to print a label and it is still asking you to pay your bill:
-Log out, clear browser cache, close out browser, then try.
-Admin has also said the system can take a few minutes to update after paying the bill...so sometimes waiting five minutes or so for the system to update will work.
Generally speaking the clear browser cache, logging out and back in may clear up a number of issues with any website. One can also try a different browser if you have another browser installed.
Of course, if there is a specific problem on the Etsy side of things none of the above will probably help at all.
@Todd--I don't mind helping when I can, I learn a lot from others that take time to share what they know. I agree, when it comes to time sensitive issues like shipping labels-- because we do need to get items shipped out and there is a tight deadline on cancelling a label---3+ days is too long to wait for a support response.
With that said...another general tip, be sure to check your junk/spam folders if you are waiting for a response from Etsy. Depending on your filters, an email from Etsy can very often end up there.
